Skillings-Mack Statistic: Computer-Intensive Methods - Srisuradetchai, Patchanok; Trakultraipruk, Nantapath (Journal of Applied Statistics and Information Technology, 2016)
The Skillings-Mack statistic is the appropriate statistic when missing observations occur randomly in a block design. In this paper, the exact randomization test and the Monte Carlo method are applied for the Skilling-Mack test statistic. We found that when there is more missing data, the chi-squared distribution is worse for being a reference distribution to calculate critical values even for significance levels near .10. Furthermore, for some designs with two missing values it is impossible to reject the null hypothesis when using the chi-squared distribution. Also, we have developed the R package named Skillings.Mack to calculate the Skillings-Mack statistic as well as produce p-values based on the Monte Carlo method. Our R package is very useful when there are many ties and/or small designs are conducted. Finally, we present tables of critical values for block designs with two missing observations.